efficient contracts with costly adjustment: short-run

Efficient Contracts with Costly Adjustment: Short-Run EmploymentDetermination for Airline Mechanics

David Card

The American Economic Review, Vol. 76, No. 5. (Dec., 1986), pp. 1045-1071.

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Efficient Contracts with Costly Adjustment: Short-Run Employment Determination for Airline Mechanics

This paper presents an empirical analysis ofjrm-spec$c employment and wage outcomes for mechanics in the domestic airline industry. A dynamic contracting model is presented that incorporates both costly employment adjustment and potential gaps between contract wage rates and the opportunity value of workers' time. The model gives a useful description of the employment-output linkage in the data, but is less successful in capturing the dynamic relation between employment, contract wage rates, and wage rates outside the airline industry.

The search for a credible interpretation of observed employment patterns has led to widespread interest in the notion of efficient labor contracts.' In contrast to traditional auction models of the labor market, whch relate fluctuations in employment directly to changes in wage rates, contracting models permit a more flexible link between wage payments and employment determination. According to the simplest version of the efficient contracting hypothesis, in fact, the level of employment maximizes the joint income of workers and the firm, whle the level of wages represents a pure transfer between them. If thls "strong form" efficiency hypothesis is correct, then it calls into question a wide variety of policy conclusions based on the assumed distortionary effects of

*Department of Economics, Princeton University, Princeton, NJ 08544. I am grateful to Robert LaLonde for his assistance in gathering the data in tlus paper, and to Jim Brown, John Pencavel, and an anonymous referee for comments on earlier drafts.

'The theoretical literature on efficient contracting is voluminous: see in particular Wassily Leontief (1946), Costas Azariadis (1975), Martin Baily (1974), Donald Gordon (1974), Robert Hall and David Lilien (1979), Ian McDonald and Robert Solow (1981), and the recent surveys by Oliver Hart (1983) and Sherwin Rosen (1985). Jan Svejnar (1986) presents an empirical study of efficient wage and employment outcomes. James Brown and Orley Ashenfelter (1986), Thomas MaCurdy and John Pencavel (1986), and F. Martinello (1984) attempt to test between efficient contracting models and conventional employment-setting models.

union wage differentials and short-term wage rigidities.

A simple test of the efficient contracting hypothesis is provided by a firm-level employment equation that includes both the wage rate at the firm and some measure of the alternative wage available to workex3 According to the strong form efficiency hypothesis, the joint income of workers and the firm is maximized when the marginal value product of labor equals its outside opportunity wage. If this hypothesis is correct, employment is independent of firm-specific wage rates and depends only on the alternative wage rate. In the traditional labor demand model, by comparison, the firm's prof- its are maximized when the marginal value product of labor equals the firm-specific wage. If this model is correct, then employment is independent of alternative wage rates and depends only on the firm's wage rate. Finally, in a general contracting model, labor is allocated between outside opportunities and contract employment on the basis of a shadow value that varies with both firm-specific and alternative wage rates.

'This point was made forcefully by Robert Barro (1977) in a comment on models of nominal wage contracting.

3 ~ h i sis essentially the test procedure adopted by Brown and Ashenfelter. MaCurdy and Pencavel estimate a capital-labor ratio equation that includes both contract and alternative wage rates.

1046 T H E A M E R I C A N E( ' O N O M I C REVIEW D E C E M B E R 1986

In a dynamic setting, however, tests of even simple efficient contract models are complicated by the fact that alternative wage rates may help to predict future contract wage rates. Suppose, for example, that employment adjusts toward a target level that depends on a weighted average of future contract wage rates. In t h s case, even if desired employment is independent of alternative wages, current and lagged alternative wage rates may enter the employment equation as predictors of future contract wages.

In a dynamic model it is therefore neces- sary to sort out two competing routes for the alternative wage to influence the level of contract employment: ( i ) directly, through the appropriate expression for the shadow value of labor; and ( i i ) indirectly, through the statistical link between current alternative wage rates and expected future contract wage rates.

Thls paper presents an empirical analysis of the potential links between wage rates and employment for mechanics in the domestic airline industry. The data consist of quarterly observations on employment, output, and wages for seven major airlines, drawn from the period prior to deregulation of the industry. Wage rate information is taken from union contracts covering mechanics at each of the seven airlines, whle employment and output data are taken from Civil Aeronautics Board records.

Section I presents a preliminary analysis of the data using unrestricted vector auto-regressions. The analysis reveals a strihng similarity between the serial correlation properties of these micro-level data, and the properties of more familiar aggregate data. The analysis also shows that aggregate manufacturing wage rates are an important determinant of both employment levels and wage rates for airline mechanics. On the assumption that the manufacturing wage rate represents the alternative wage rate for airline mechanics, the observed link between me-chanics' employment and manufacturing wages can be attributed either to efficient contracting considerations, or to the fact that manufacturing wages help predict future contract wage rates, or both.

The second section of the paper presents a simple intertemporal contracting model in whlch it is possible to disentangle these two effects. The model assumes that employment and wages are selected to minimize the cost of aircraft maintenance, subject to a utility constraint for mechanics. Adjustment costs are introduced on the firm's side to generate an employment function with serial per-sistence and gradual adjustment to output shocks. Two specifications of workers' preferences are presented that yield alternative expressions for the shadow value of labor in an optimal contract. The traditional labor demand model and the strong form efficient contracting model are obtained as special cases of the general model.

The model yields a partial-adjustment employment equation that expresses current employment in terms of lagged employment, lagged departures, and lagged wage rates. The model generates testable restrictions across the employment equation and the forecasting equations for output and wages, and summarizes the employment effects of alternative wage rates in terms of two components: a direct effect on the desired level of employment; and on indirect effect on forecasts of future contract wages.

Section I11 presents the results of fitting the model to data on departures, wages, and employment for the seven airline firms. The empirical analysis is generally unsupportive of either the strong form efficient contracting model or the labor demand model. Both models are rejected in favor of a more general contracting model in which the opportunity cost of employment is a weighted average of the contract wage and the alternative wage. The parameter estimates for all three models are poorly determined, however, and the implied reduced forms fail to reconcile all the dynamic linkages between contract wages, alternative wages, and employment.

I. Preliminary Data Analysis

The data in this paper consist of quarterly observations on employment and wages for aircraft mechanics employed in the domestic

VOL 76 VO 5 CARD EFFICIENT CONTRACTS W I T H C O S T L ) ADJCSTWE? T 1047

operations of seven airlines: American, Braniff, Continental, Eastern, Trans World, United, and ~ e s t e r n . ~ earn-Employment, ings, and flight data were collected from various Civil Aeronautics Board (CAB) sources for the period 1969:I to 1 9 7 6 : 1 ~ . ~ Wage rates were collected from union con-tracts summarized in Current Wage Deuelop- ments and the Bureau of National Affairs' Daily Labor ~ e ~ o r t . ~ A complete description of data sources is provided in Appendix 11.

Mechanics at these airlines are repre-sented by three unions: the Transport Workers Union (TWU) at American; the Teamsters (IBT) at Western; and the Ma- chinists (IAM) at the other five airlines. Al- though the IAM bargained individually with these five airlines during the sample period, contract terms and expiration dates differed little between them. Differences among the IAM contracts were due mainly to delays in signing new contracts at the individual airlines.'

4Data are also available for three other domestic trunk airlines-Delta. National, and Northwest-as well as for Pan Am. Because of the high level of strike activity at National and Northwest, these airlines were excluded from the present study. Pan Am diKers from the domestic trunks in that a large share of its business is international. For t l s reason, domestic employment data for Pan Am may be misleading, and I chose to exclude it. Delta's mechanics are nonunionized and, as a result, no direct measure of contract wage rates is available.

*Detailed quarterly employment data are unavailable after 1976. Employment and payroll information pertain to maintenance and related workers, as defined by the CAB. This group includes aircraft inspectors and mechanics. as well as cleaners, janitors, and stock clerks. According to CAB records. there were 37,036 maintenance workers in the domestic trunk airlines in the t l r d quarter of 1975. A Bureau of Labor Statistics (BLS) It~dutrn: Wage Suruev during August-November 1975 counted 29,518 inspectors and mechanics, and 8,588 cleaners, janitors and stock clerks at the domestic trunks, for a total of 38,106 maintenance and related workers. O n t h s basis, approximately 80 percent of maintenance workers are actually airline mechanics or inspectors.

Wage rates for mechanics at Western Airlines were obtained from copies of the contracts generously made available to me by the IBT Airline Division.

' ~ u r i n g this period the delay between expiration of old contracts and renegotiation of new contracts was typically six to twelve months.

Table 1 presents annual data on nominal and real wage rates for airline mechanics at the various firms between 1969 and 1976.8 There were only small and unsystematic differences between wage rates negotiated by the three unions. Compared to other workers, however, airline mechanics earned relatively hlgh wage rates during thls period: 50 to 60 percent higher than average straight-time hourly earnings in manufacturing, for example, and about 25 percent higher than average hourly earnings reported by mainte-nance mechanics in manufacturing. Airline mechanics also earned a small premium (5 to 15 percent) over unionized mechanics at the major aircraft companies.

Airline mechanics' nominal wage rates are established in two- or three-year contracts that typically include both noncontingent deferred increases and cost-of-living al-lowance clauses. During the sample period, new agreements were negotiated in 1969 (from March to December, depending on airline), 1971-72 (May 1971 to December 1972), 1973-74 (November 1973 to August 1974), and 1975-76 (December 1975 to Sep- tember 1976). Because of deferred increases and cost-of-living adjustments, however, the relation between contract negotiations and real wage rates is indirect. Real wage rates increased over the term of the 1969 contracts, for example, but were more or less constant between 1973 and 1976.

The behavior of real contract wage rates is analyzed more formally in Table 2. Column 1presents a simple second-order autoregression (AR(2)) fit jointly to the logarithms of contract wage rates for all seven airlines, with unrestricted constants, trends and seasonal dummy variables for each airline.9 As is apparently true for aggregate real wage

'Wage rates in Table 1 are for certified mechanics, excluding premiums for line service work (10 to 25 cents per hour during t l s period) and FAA licenses (10 to 20 cents per hour per license). Wage rates for mechanics represented by the IAM are summarized by the wage rates at United Airlines.

'A simple F-test that the AR(2) coefficients in the wage equation are the same across all seven airlines yields a probability value of .04. The major difference in coeficients is between American and the other airlines.

1048 T H E A WERICAN ECONOMIC REVIEW DECEMBER 1986

TABLE1-WAGE RATES FOR AIRLINEMECHANICS GROIJPS:1969-76AND COMPARISON

Maintenance Production Licensed American- United- Western- Mechanics in Workers in Mechanics

TWUa I A M ~ ~ a n u f a c t u r i n ~ ~IBT' Manufacturinge B O ~ ~ ~ ~ - I A M '

1969 4.60 4.40 4.47 3.77 3.07 4.46 [4.60] [4.40] [4.47] [3.77] [3.07] [4.46]

1970 5.10 5.20 5.27 3.98 3.24 4.65 [4.81] [4.91] [4.98] [3.76] [3.06] [4.39]

1971 5.60 5.60 5.68 4.24 3.44 4.90 [5.07] [5.07] [5.14] [3.84] [3.11] [4.44]

1972 6.20 5.95 5.98 4.56 3.65 5.38 [5.43] [5.21] [5.24] [4.00] [3.20] [4.71]

1973 6.40 6.60 6.45 4.84 3.90 5.78 [5.28] [5.44] [5.32] [3.99] [3.22] [4.77]

1974 6.85 7.10 6.85 5.22 4.23 6.16 [5.09] [5.28] [5.09] [3.88] [3.14] [4.58]

1975 7.50 7.70 7.70 5.97 4.65 7.03 [5.10] [5.24] [5.24] [4.07] j3.171 14.791

1976 8.10 8.45 7.90 6.54 5.00 7.53

Notes: Real wage rates represent nominal rates divided by the CPI, all items. 1969 =100. In each colun~n, real wage rates are shown in brackets below nominal rates.

"Average base rate in effect for mechanics in collective agreement between American Airlines and Transport Workers Union.

b ~ v e r a g e base rate in effect for mechanics in collective agreement between United Airlines and Machinists Union. Wages for mechanics at Braniff, Continental, Eastern, TWA, and United are similar.

'Average base rate in effect for mechanics in collective agreement between Western Airlines and Teamsters Union.

d ~ v e r a g e hourly earnings of maintenance mechanics in manufacturing, from the BLS Area Wage Survey.

'Average straight-time hourly earnings of production workers in manufacturing, annual averages of quarterly values.

' ~ v e r a ~ ebase rate in effect for licensed aircraft mechanics in collective agreement between Boeing and Machinists Union from the BLS Wage Chronology.

rates, the contract wage for airline mechan- Columns 2, 3, and 4 of Table 2 contain ics is approximately a first-order autoregres- estimates of real wage regressions that in- sive process, with something less than a unit clude lagged values of manufacturing wages autoregressive coefficient.1° For purposes of and consumer prices. Each of these two ag- comparison with the results from a longer gregate series has strong causal links to con- sample period, column 6 of the table pre- tract wages. The point estimates in column 2 sents the same remesentation of contract show that a permanent 1 percent increase wage rates fit to an' extended sample period in manufacturing wages leads to an eventual (1964 to 1978). The addition of seven extra increase in contract wages on the order of years of data has no appreciable impact on 1 percent, whlle the estimates in column 3 the estimated coefficients, however. suggest that a permanent increase in prices

leads to a permanent decrease in contract wages. In column 4, both prices and manufacturing wages are entered in the regression

'Osee, for example, Ashenfelter's and my paper for contract wages. Although the statistical (1982). A similar specification fit to real straight-time significance of the individual coefficients is average hourly earnings in manufacturing over this sample period yields a first-order coefficient of 1.09 (with a mixed, a test that lagged consumer prices standard error ( S E ) of .20) and a second-order coeff- improve the forecast of contract wages, given cient of - .26 (SE =20) . lagged manufacturing wages, is marginally

VOI. 76 NO 5 CARD EFFICIENT CONTRACTS WITH COST12? ADJCSTMEX T 1049

Contract Real Wage: 1969:III-1976:IV

(1) (2) (3) (4) (5)

Contract Wage .71 ( t - 1 ) (.08)

Contract Wage - .04 ( r -2) ~ 0 7 )

Manufacturing -

Wage ( t - 1) Manufacturing -

Wage ( t -2) Price Index -

( 1 - 1)Price Index -

( t -2) Employment -

( t - 1 )Employment -

( t - 2 ) Probability Value for Exclusion of:

Manufacturing Wage -

Consumer Prices -

Contract Real Wage. 1964:III-1978:IV

(6) (7) (8) (9)

Notes: Regressions include constants, linear trends. and quarterly dummy variables. Coefficients (except constants, trends, and seasonals) are restricted to be equal across airlines. Contract wages and manufacturing wages are deflated by the Consumer Price Index. Regressions contain airline-specific dummy variables for strike and immediate poststrike observations.

"The standard errors are shown in parentheses.

significant, whlle a test for lagged manufacturing wages, given lagged prices, is not quite significant at conventional levels. Parallel results for the longer sample period (in cols. 7, 8, and 9) lead to very similar conclusions.

Finally, column 5 reports the coefficients of lagged employment in forecasting con-tract wages. The point estimates suggest that increases in employment lead to small increases in real contract wages, although a test of the hypothesis that employment fails to Granger-cause wages is not significant at conventional levels."

The general pattern of employment for airline mechanics is illustrated in Figure 1, whch gives a time-series plot of departures and employment at American Airlines. In addition to mechanics' employment, the figure shows quarterly employment levels for pilots and flight attendants. One of the most interesting features of the data is the extent

h he probability value of the test statistic is 0.12

to whlch employment of these three groups of workers is smoothed vis-a-vis departures. At one extreme, the number of employed pilots is very stable and shows little relation to output. At the other, the number of flight attendants is quite variable over time. Me- chanics fall somewhere between these two groups. Fluctuations in departures translate into dampened fluctuations in the number of employed mechanics.

Data on flying operations and mechanics' employment are summarized by airline in Table 3. The airlines fall naturally into two groups: the four largest firms- American, Eastern. Trans World. and United-and the three smaller firms. Interestingly, the number of mechanics per unit of output is quite different between the larger and smaller airlines. Relative to the employment levels at the smaller airlines, the larger airlines have 60 to 70 percent more maintenance em-ployees per departure (or per available seat mile). To some extent t h s may reflect a greater reliance on outside contractors to

1050 T H E AMERICAN ECONOMIC REVIEW DECEMBER 1986

perform specialized maintenance operations at the smaller airlines. Smoothing of employment relative to departures is indicated by the smaller coefficient of variation of em-ployment for all the airlines except Con- tinental and United. A similar conclusion emerges from a comparison between de-trended and deseasonalized employment and departures. With the exception of United Airlines, the standard deviation of the logarithm of employment is about two-thirds as large as the standard deviation of the logarithm of departures, when both series have been fitted to a linear trend and quarterly dummy variables.

Table 4 presents a more formal analysis of employment variability and its relation to departures and wages. Column 1 presents a simple AR(2) specification of employment, fit jointly to the seven airlines with firm- specific trends, constants, and seasonals. Employment of airline mechanics displays the hump-shaped moving average representation that characterizes many aggregate employment time-series.12 The response to a unit innovation in employment persists for

'*see Thomas Sargent (1978), for example.

VOL. 76 NO. 5 CARD: EFFICIENT CONTRACTS W I T H C O S T L Y ADJL'STMENT 1051

TABLE3-MEANS DEVIATIONS: AIRLINEDATA 1969:I-1976:IV AND STANDARD DOMESTIC

American Braniff Continental Eastern TWA United Western

Average Quarterly Departures

Standard Deviation of Departures

Average Quarterly Maintenance Employment

Standard Deviation of Employment

Average Number of Seats per Flight

Average Flight Length

Coefficient of Variation of Departures

Coefficient of Variation of Employment

Ratio of Coefficients of Variation- Employment/Departures

Standard Error of Detrended-Deseasonalized Log Departures

Standard Error of Detrended-Deseasonalized Log Employment

Ratio of Standard Errors- Employment/Departures

Notes: Data pertain to domestic operations. Data from quarters with strike activity are removed. The following airlines had strikes during the sample period: American (1969:I), Continental (1976:IV), TWA (1973:IV), United (1975:IV) and Western (1969:III). All data are from CAB published and unpublished sources.

roughly ten quarters. As one might expect turing wages is stronger. Finally, column 5 from Table 3, there is some heterogeneity includes both wage measures together. In across the airlines in the autoregressive rep- t h s equation, increases in contract wages resentation of employment, particularly be- have a significantly negative effect on em-tween United and the other six carriers. An ployment, whereas increases in manufac-F-test that the coefficients are the same across turing wages lead to an eventual increase in the seven airlines yields a probability value employment.13 of just under .001. The results in column 5 are apparently

Column 2 of Table 4 presents the coeffi- robust to several alternative definitions of cients of two lagged values of departures in the opportunity wage for airline mechanics. explaining maintenance employment at the In particular, if the manufacturing wage is seven airlines. The coefficients are individu- replaced by the average wage of mainte-ally significant at conventional levels, al- nance mechanics in manufacturing (inter- though their joint contribution, summarized polated from annual BLS Area Wage Survey by the probability value in the last row (c), is only marginally significant. Columns 3 and 4 examine the role of lagged contract wages

comparable regression of employment on con- and lagged manufacturing wages in predict- 1 3 ~

temporaneous departures, contract wages, and manu-ing employment. The evidence that contract facturing wages yields a coefficient for contract wages of wages influence employment is relatively - ,034 ( S E = .045) and a coefficlent for manufacturing weak, although the evidence for manufac- wages of ,061 ( S E = ,138).

TABLE 4-AUTO~GRESSIVE SIONS OF E\IPI.OY~CENT~~ P R E S E N ' T A

Dependent Variable: Logarithm of Maintenance Employ~nent

(1) ( 2 )

1.16 1.09 (.06) i.06) - .42 - .34 ~ 0 7 ) (.07)

( 3 )

1.09 (.06) - .34

t.06) .13

(.04) - .09

(.04) .02

(.04) - .Oh (.04) -

-

.04

.27 -

14) ( 5 )

1.09 1.08 (.06) 1.06) - .36 - .36 (.06) (.06) .14 .13

(.04) (.04) - . l l - .09

(.04) 1.04) - - .01

(.04) - - .10

1 04) - .28 - .24 i.16) ( . l h ) .46 .53

(.I61 (.16)

.04 .04 - .01 .03 .02

Employment ( 1 - 1 )

Employment ( 2 - 2 )

Departures ( t - 1 )


Contract Wages ( 2 - 1)

Contract Wages ( 2 - 2 )

Manufacturing Wages ( t - 1)

Manufacturing Wages ( t - 2 )

Probability Value of Exclusion Test for:

(a ) Departures ( b ) Contract Wages

-

-

-

-

-

-

-

-

.12

- .10 (.04) -

-

-

-

.05 -

-(ci Manufacturing Waees -

Nores: All regressions include constants, trends, and quarterly dummy variables. Coefficients (except constants, trends, and seasonals) are restricted to be equal across airlines. Wage rates are deflated by the CPI. The probability values in the last row (a)-(c) refer to an F-test for the joint significance of two lagged values of the indicated variable.

aThe standard errors are show-n in parentheses.

data) or the wage rate for licensed mechanics at Boeing (available from the BLS Wage Chronology series), the coefficients are very similar in size and magnitude to those in Table 4, although less precisely estimated. I also constructed airline-specific measures of the opportunity wage based on earnings of maintenance mechanics and unemployment rates in cities where each airline has its major maintenance base.14 These alternative wage measures give the same pattern of results as the manufacturing wage rate, although each can be rejected as a significant determinant of maintenance employment after controlling for the manufacturing wage rate. In thls

141f the appropriate opportunity wage is the wage on an alternative job multiplied by the probability of being offered that job. then an observable proxy for the opportunity wage is (1- U ) a , where U is the relevant unemployment rate and a is the wage rate of maintenance mechanics in the relevant city. This wage index was suggested by Brown and Ashenfelter.

paper I therefore use the manufacturing wage as the alternative wage rate for airline mechanics.

Table 5 examines the contribution of several additional explanatory variables for maintenance employment. In each case, the employment equation contains two lagged values of the explanatory variable listed in the column heading. together with lagged values of employment, departures, contract wages, and manufacturing wages. The first four columns present employment equations that include alternative aggregate variables: consumer prices, real national income, an index of CAB-regulated passenger fares, a jet fuel price index, and an index of parts prices. None of these variables significantly improves the prediction of employment, maintaining lagged departures and wage rates. The next five columns report employment regressions that include additional airline-specific measures of output: available seat miles, revenue-passenger miles, domes-

1053 VOL. 76 NO. 5 CARD. EFFICIENT CONTRACTS WITH COSTLY ADJUSTME,VT

TABLE5-ADDITIONAL MODELSAUTOREGRESSIVE OF EMPLOYMENT

Additional Explanatory Variable Included in Employment Regression

Output Fuel Parts Available Revenue Domestic Total Consumer

Prices Real GNP

Price Indexa

Price 1ndexb

Price Index'

Seat Passenger ~ i l e s ~ Milese

Flight ours'

Flight Hoursg

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Employment ( t - 1)

Employment ( t - 2 )

Departures ( t - 1)

Departures (1 -2)

Contract Wages (1-1)

Contract Wages ( t -2)

Manufacturing Wages ( t - 1)

Manufacturing Wages ( t -2)

Added Variable ( t - 1 )

Added Variable ( t -2)

Probability Value for Exclusion of Added Variable

Notes: See notes to Table 4. The standard errors are shown in parentheses. "Price index of domestic passenger fare rates set by CAB (constructed by the author). bPrice index for jet fuel (constructed by the author). 'Price index for commodity group 14: miscellaneous parts and machnery. *~vailableseat miles on scheduled domestic passenger routes. eRevenue passenger miles on scheduled domestic passenger routes. 'Aircraft revenue hours in domestic service. including nonscheduled, freight, and scheduled passenger senlice gAircraft revenue hours in domestic and international service.

tic flight hours, and total flight hours (in- nally, while the results are not recorded in cluding domestic aild international flight the table, I have also computed employment hours). Apart from available seat miles, none regressions that include airline-specific fleet of these output measures is an important composition variables.'' Although these determinant of employment, once the level measures of firm-specific capital stock are of departures is taken into account. Depar- margnally significant determinants of em-tures and available seat miles are hlghly co- ployment, their inclusion has no effect on linear, however, and the sums of the coeffi- the nature of the results in Tables 4 or 5. cients on departures and seat miles are very The analysis of employment in Tables 4 nearly equal to the corresponding coeffi- and 5 is restricted to the number of mechan- cients of departures when seat miles are excluded from the regression. Since the coefficients of the other variables are not much '5~irline-specific fleet composition data are available

affected by the presence or absence of seat on a annual basis from the Federal Aviation Adminis- tration Statistical Handbook of Auiation. For purposes

miles in the employment equation, I use of the employment regressions, I interpolated the num- departures as the sole measure of airline ber of aircraft of each type of airline by quarter, and output in the remainder of the paper. Fi- grouped aircraft into five types.

1054 T H E AMERICAX ECONOMIC RE1'IECI DECEMBER 1986

TABLE6-AUTOREGRESSIVEREPRESENTATIONSO t DEPAKTURES

Additional Explanatory Variable Included in Departures Regression:

Manufacturing Consumer None Em~lovment Real G N P Wace Prices

Departures ( 1 - 1)


Added Variable ( t- 1)

Added Variable ( t - 2 )

Probability Value for Exclusion of Added Variable

Notes: See notes to Table 4. The standard errors are shown in parentheses

ics on airline payrolls in each quarter. A more complete description of labor inputs, however, requires information on hours per employed worker. Although CAB records do not include a direct measure of hours per worker, a noisy indicator of hours is available from data on average payroll cost per worker. Specifically, the ratio of payroll cost per worker to the contract wage rate represents the sum of straight-time hours per worker, average overtime hours per worker (weighted by the overtime wage premium), and fringe benefit costs per worker (ex-pressed as a fraction of the straight-time wage rate).16 A regression of t h s hours index on contemporaneous employment and departures reveals no significant correlation with either variable." This absence of corre-

l h ~ e tE represent payroll cost per worker, let w represent the union wage scale, let h , and h , represent average straight-time and overtime hours per worker, respectively, and let g represent average fringe benefit costs per worker, then

where w represents the average overtime wage pre-mium. The ratio of payroll cost to the contract wage rate is therefore

he coefficient on the logarithm of employment is .06 ( S E =.06) and the coefficient on the logarithm of departures is .02 ( S E = .05).

lation suggests that measured hours variation can be safely ignored in the study of employment and output.

The interpretation of employment equations that include lagged output variables, such as those in Tables 4 and 5 , depends critically on the time-series representation of output. Table 6 presents several alternative representations of the level of departures activity at the seven airline firms. In each case the logarithm of departures is regressed on two lagged values of departures and two lagged values of the explanatory variable listed in the column heading. The coefficient estimates of a univariate forecasting equation (col. l) show that departures have a monotonically declining moving-average representation, rather than the hump-shaped representation that characterizes employ-ment. Column 2 presents the coefficients of lagged employment in a forecasting equation for departures, as well as the probability value of the associated exclusion test. The hypothesis that departures are exogenous to maintenance employment is not rejected at conventional significance levels. Columns 3-5 present the coefficients of three alternative aggregate variables in the departures equations: real output, manufacturing wages, and consumer prices. None of these is significantly related to departures activity, however, controlling for lagged departures.

VOL. 76 NO. 5 CARD. EFFICIE,VT CONTRACTS M'ITH C0STI.Y A DJUSTMENT I055

To conclude this preliminary data analysis, the main conclusions may be summar-ized as follows:

1) The serial correlation properties of firm-specific employment and wage data for airline mechanics are very similar to the properties of aggregate data. Airline me-chanics' real wage rates follow a first-order autoregressive process, whle their employment levels follow a second-order process.

2) In the period under study, wage rates of airline mechanics were very similar across firms and uncorrelated with firm-specific employment levels. Real wage rates were sig-nificantly correlated with lagged manufacturing wage rates and lagged consumer prices.

3) Employment of airline mechanics is correlated with lagged values of contract wage rates and lagged values of wage rates outside the airline sector. The separate effects of these two wage rates are well-determined and in opposite directions. The employment effect of outside wage rates is apparently robust to alternative definitions of the outside wage, although average hourly earnings in manufacturing have the strongest correlation with employment of airline mechanics.

Building on these conclusions, the next section presents an intertemporal contracting model that provides a framework for testing between alternative models of the link between wage rates and employment.

11. Contractual Employment with Costly Adjustment

This section presents a simple extension of the static efficient contracting model to an intertemporal setting. Adjustment costs are introduced on the firm's side in order to generate an employment function with serial persistence and cumulative rather than instantaneous responses to changes in output or wages. The resulting function ex-presses optimal employment in terms of lagged values of employment, output, and wages, and provides a convenient framework for testing alternative models of employment determination. Both the labor demand model of employment determination, in which the

employer takes contract wages as given, and the strong form efficiency model, in which the marginal product of labor is equated to the alternative wage rate, are obtained as special cases of the model. In contrast to tests of the efficient contract hypothesis based on a static employment function, the time- series correlations of employment and wages are modeled explicitly, and used to disentangle the forecasting role of alternative wages from any efficient contracting effects.

For simplicity, the dynamic relationshp between output, wages, and employment is assumed to arise solely from the demand side of the contract. Workers are modeled as having separable preferences over time, with no interaction between lagged values of wages or employment and the ranking of current wage-employment pairs. Whlle this assumption simplifies the analysis and interpretation of the dynamic employment function, it restricts the role of lagged wages and employment in generating current employment, and represents an obvious channel for further research.''

The first step in specifying the contractual employment function for airline mechan-ics is to specify the link between flight activity, maintenance activity, and employment. Airline mechanics service and inspect aircraft between departures ("line service") and also rebuild and overhaul aircraft components at major service intervals.19 In either case, a variety of substitutes is available for in-house mechanics' services, including outside sub- contractors and purchases of new parts and equipment. In addition, airlines can sub-stitute mechanics' services over time by add-

I81f workers bear mobility costs of moving between contract and alternative employment than presumably these costs should be internalized in an optimal employment contract. Alan Carruth and Andrew Oswald (1985) discuss the formulation of workers' objectives in an intertemporal contracting model.

19Each of the seven airlines in this study maintains a major maintenance depot where airframes and engines can be dismantled and rebuilt. In the industry as a whole, mechanics are more or less evenly split between line service and major maintenance activities.

10.76 T H E AMERICAN EC - 0 N O M I C RE C'IE W DECEMBER 1986

ing to or running down the stock of airworthy equipment. For simplicity, however, I as-sume that a given level of flight activity in the t th quarter, F,, requires a proportional input of maintenance activities. I also as-sume that that maintenance is produced by a combination of in-house employment N, and other inputs M I , according to a Cobb-Douglas production function

where y, and y, are positive constants and A is a constant depending on aircraft type and route structure. The direct cost of maintaining a level of flight activity F, with a labor force of N, mechanics is therefore

where w , is the contract wage for mechanics, q, is the price of other maintenance inputs,

x , then preferences of a representative worker are summarized by

= -u (w, , v, + 1-- u ( a , v,). No

In the second case, following John Pencavel (1984), assume that workers' preferences can be summarized by a Cobb-Douglas function of employment and the gap between con-tract and alternative wages:

Both of these specifications contain as a special case the "excess earnings" objective N,( w ,- a , ) associated with an income-maxi- rnizing union. 20

Under the assumption that current and and r(N, , 4 ) A - ' / Y z N ~ - Y ~ / ~ ~ F , ~ / ~ ~the future flight activity are exogenous to main- = is input requirement function for nonlabor inputs, given labor inputs N, and output F,.

In addition to these direct costs. I assume that the firm bears an adjustment cost J ( N t , N, - ,) in period t that depends on the level of employment in t and t -1. This adjustment cost captures both hiring and firing costs, and the cost of rearranging flight schedules as the number of employees available for line service at each airport is ad- iusted over time.

The final ingredient of the employment contract is the specification of workers' preferences. I assume that preferences in each period are represented by a function of contract wages, employment, outside or alternative wages a,, and a random preference shock v,: U(N, , w ,,a ,,v,). Two functional forms are considered-for U . In the first case, assume that No workers are attached to the firm, and that workers are allocated randomly in each period between contract employment and alternative employment with probabili- ties N,/No and 1- N,/No, respectively. If u ( x , v,) is a von Neumann-Morgenstern utility function defined on the level of earnings

tenance employment, an optimal contract minimizes the expected present value of employer's costs, subject to an expected utility requirement for workers. Assuming that employers and workers have a constant discount rate p ( p < I), the level of employment and wages in period t solves

subject to

'O~or the expected utility specification, set a ( x , , v,) = x,. For the Cobb-Douglas specification, set k ( v , )=l and 0, = 0, = 1. Income maximization is an appropriate objective for workers as a group if there are no con- straints on the internal distribution of earnings or employment opportunities among the group.

1057 VOL,. 76 NO. 5 CARD: EFFICIENT CONTRACTS WITH COSTLY ADJUSTMENT

In these expressions expectations (denoted E ) are taken over the joint distribution of the entire sequence of future flight activity, input prices, alternative wages, and preference shocks. The solution to t h s con-strained-optimization problem can be ob-tained as the solution to the Lagrangan expression

for some positive constant p. In contrast to the efficient contracting

model, whch views employment and wages as jointly determined, the traditional labor demand model treats employment as de-termined unilaterally by the firm, talung contract wages as given. In t h s case, observed employment solves the employer's cost-minimization problem

directly, subject to the forecasting equations for flight activity, input prices, and contract wages. A comparison of equations (5 ) and ( 6 ) reveals two important differences between the efficient contract and labor demand models. First, the efficient contract model treats wages and employment as jointly endogenous. Second, whle alternative wages enter the contracting model directly through workers' preferences, in the labor demand model the only role of alternative wages is in the forecasting equation for future contract wages.

Before deriving the employment functions associated with the contracting and labor demand models, it is useful to characterize

the wage function implied by the efficient contracting model. In particular, it is interesting to ask if a contracting model whch considers wages and employment as jointly determined can ever lead to the prediction that wage outcomes are independent of pre- vious employment levels. The empirical analysis in Section I suggests that t h s is an important characteristic of contract wage rates for airline mechanics.

The first-order condition for wages in period t + j for the contracting model (5) is

From this equation it is evident that the choice of contract wages in t + j is independent of employment if workers' preferences are linear in employment: say,

U ( N ,w , a , v ) = N f ( w , a , v).

In that case, the first-order condition (7) has the simple form

with the implication that contract wages are determined in each period independent of employment or wage choices in any other period. Since the evidence in Section I suggests that contract wages are unrelated to past employment, the assumption that workers' preferences are linear in employment is plausible as well as convenient, and will be adopted here. The expected-utility preference specification (3) imposes linearity a priori21 For the Cobb-Douglas specification (4), linearity implies a within-period objective of the form N,(w, - a,)', where 8 = 8, > 0 may be either greater than or less than unity.

21The expected utility preference specification is linear in employment under the assumption that the probability of employment is proportional to the actual level of employment.

1058 T H E AMERICAN ECONOMIC R E V I E W DECEMBER 1986

Specializing the first-order condition (7) to these two preference specifications leads to

in case of expected utility preferences, and

in case of Cobb-Douglas preferences. The expected utility specification implies that real contract wages are constant over time, apart from changes in the preference shock v or random measurement errors. The Cobb-Douglas specification, on the other hand, suggests that contract wages maintain a constant (absolute) differential over alternative wages. For example, if k(v,) = v:-' and v, is first-order autoregressive, then equation (8b) implies

where 6, is the first-order autocorrelation coefficient of v, and V; = v, - 61v,-l is serially uncorrelated. Comparison of this equation with the fitted regressions in Section I suggests that the first-order condition (8b) may provide a useful model of the contract wage determination process for airline mechanics.

The assumption that workers' preferences over employment and wage outcomes are linear in employment simplifies the analysis of contractual employment setting. Let w;+, represent the solution to equation (8a) or (8b). Since contract wages are unrelated to past employment decisions, the optimal level of contract employment in t solves

subject to the forecasting equations for flight activity, alternative wages, preference shocks,

and optimized contract wages.22 If employment fails to Granger-cause wages, the contract employment function can be obtained by talung the contract wage as exogenous. In this case, the labor demand model of em-ployment determination (6) is a special case of the contracting model (9) with p = 0,

In order to derive the contract employ-ment function when there are costs of changing employment from period to period, it is convenient to proceed in two steps. The first is to derive the optimal employment level in the absence of adjustment costs. The second is to derive the actual employment decision by comparing the costs of changing employment over time with the cost of sub- or superoptimal employment in each period.23 For simplicity, these two cost components are expressed as quadratic functions of the logarithm of employment, yielding an em-ployment function that is linear in the logarithms of employment, output, and wages.

The optimal employment choice in the absence of adjustment cost can be obtained from the first-order condition for the contracting problem (9), setting the adjustment cost component to zero:

For the expected utility specification of workers' preferences, this first-order condition implies

where for simplicity I have suppressed the dependence of v on the preference shock v,. The term on the left-hand side of this equa-

22 Since w , is a function of u , and v,, say w, = g ( u , , v,), rational forecasts for wr+, satisfy Ewr,, =

E ~ ( Q , + , >u t + , ) . 2"ohn Kennan (1979) provides a useful discussion of

this two-step procedure. *

VOL. 76 NO. 5 CARD. EFFICIENT CONTRACTS W I T H C O S T L Y A DJUSTME.\ T 10.79

tion represents the marginal value product of labor, measured by the savings in nonlabor input costs as employment is increased by one unit. The marginal value product of labor is equated to the current contract wage, minus a premium that depends on the gap between contract and alternative wages. Using the properties of the optimal contract wage (equation (Sa)), the appropriate shadow value of mechanics' labor is

If the expected utility function u is linear in earnings, then the expression for the shadow value of labor reduces to a,+,, the alternative wage rate. More generally, using a second-order expansion for u(a,+,.) around w,+/, the shadow value of labor in the absence of adjustment costs is approximately

( l l a ) St+, z a t+ , ( l + 6 n ) - 6awt+,,

where 6 is the coefficient of relative risk aversion of the utility function u(6 2 0) and

represents the average markup of the optimal contract wage over the alternative wage.24 If workers' preferences have the expected utility form, the shadow value

24Dropping time subscripts. expand v ( a ) = v ( w ) + ( a - w)c l f (w)+ : ( a - w ) 2 ~ l f ' ( w ) ,and write

[ w - a ; ( w ; a ) 2 )= w l w

where 6 = - wu"(w)/u ' (w) . Next, linearize ( (w -a ) / ~ ) ~ n , where is the average markup of around n w over a :

Substituting this expression into the expression for S and assuming that n 2 is neglible yields S = a ( l + 6 n )-w a n .

of labor in an optimal contract is decreas- ing in the contract wage. As noted by Ian McDonald and Robert Solow (1981), thls specification of workers' preferences implies that efficient combinations of employment and wages are positively correlated across otherwise identical contracts.

For the case of Cobb-Douglas preferences, the first-order condition for employment in the absence of adjustment costs is

Again, the shadow value of labor in the optimal contract is lower than the contract wage. Using the first-order condition (8b) for the optimal contract wage in period t + j , the shadow value of labor is

For values of 0 less than unity, this expression is identical to (lla). For values of 6' in excess of unity, however, the Cobb-Douglas specification implies that St is increasing in both the contract and the alternative wage.

In view of the similarity of ( l l a ) and ( l lb ) , it is straightforward to derive the optimal level of employment in period t for either specification of workers' preferences. Assuming that arithmetic and geometric averages of contract and alternative wages are equal, the logarithm of the appropriate shadow value of labor is

where a =1- 1/0 in the Cobb-Douglas specification of workers' preferences, and a = - n6 in the expected utility specification. In a strong form efficient contract where workers' objectives are summarized by the value of "excess earnings," N,(w, - a,), a = 0. In the labor demand model, on the other hand, the relevant opportunity cost of labor is the contract wage and a =1. Substi-


tuting equation (12) into the first-order condition for employment in the absence of adjustment cost and taking logarithms yields the optimal employment level

(13) log N,* = constant + b, log F,

where b, = l/(y, + y,), b2 = - cuY,/(Y, + ~ 2 ) r b3 = -(1- @)YZ/(Y~ b, =+ YZ), and y2/(yl + y2). In effect, N,* is the level of employment observed on the firm's labor demand curve when output is F, and the wage rate is a weighted average of the alternative wage a , and the contractual wage

25W ,. The cost of maintaining a level of flight

activity F, with a labor force N, # N,* can be obtained from a second-order expansion of the appropriate cost function. Let

denote the cost (net of the contribution to workers' utility) of maintenance activities in quarter t , excluding adjustment costs. Using the fact that cf(N,*) = 0,

where c,, represents a second-order expansion coefficient when deviations of N, from N,* are taken in proportionate terms.26 I assume that this approximation continues to hold when el, is replaced by its sample average value c,.

25Equation (13) can also be written in terms of alternative wages and the preference shock variable v, using the first-order condition for contract wages. For purposes of forming forecasts of future values of N,*, however, it is convenient to express the employment equation in terms of w,, since the forecasting equation for w , is directly observable.

"1n the Cobb-Douglas case, c,, is proportional to the value of nonlabor inputs at the optimal level of labor inputs.

The optimal employment choice in period t can be obtained by combining the preced- ing expression with the adjustment cost terms J(N,+ ,N, ,,-,). For convenience I assume that the costs of changing the labor force are related to the proportional change in em-ployment by

The assumption of equal adjustment costs for equiproportional increases and decreases in employment is particularly restrictive, but is required for empirical tractibility.

With this setup, it is straightforward to derive the dynamic employment equation for airline mechanics. The choice of current employment minimizes the following quadratic expression:

The solution to t h s class of problems is well-known and can be summarized by the partial-adjustment equation

where X is a root to the quadratic equation

lying between 0 and 1. According to equation (15), observed employment represents a

1061VOL. 76 NO. 5 CARD: EFFICIENT CONTRACTS WITH COSTLY A DJtiSTME.\ T

weighted average of last period's employment and the discounted average of expected future values of N,*. The adjustment parameter h reflects the relative size of the coefficients c, and c,. The larger is c,, the more costly is labor force adjustment, and the larger is

The solution for N, can be obtained by substituting from equation (13) for log N,* into (15). The resulting expression translates log N, into a function of log N,- , , and discounted averages of expected future values of log F,, log w,, log a,, and logq,. These expressions can in turn be written as functions of current and past values of wages and departures, and current and past values of all variables useful in predicting wages or departures.

The presence of unobserved error components in the static employment function (13) introduces an additional consideration into the formulation of the dynamic employment function. Suppose that equation (13) con-tains a stochastic productivity effect &,. Then, excluding constants, the dynamic employment function is

(16) log Nt = 1% N,1 + (1-A)(' - h/3 ) a

X C ('b)", [bllog ~ , + j+ bllogw,+j ] = o

+ b3loga,+, + b,logq,+, + &,+,I. An empirically useful hypothesis is that the error component E, is first-order autoregres- s i ~ e . ~ ~In particular, let

where 6 , is serially uncorrelated, and strictly exogenous to flight activity, employment or

he adiustment ~ a r a m e t e r X is related to the ratio of c, to c, by c,/c, = (1- h ) ( l - X P ) X - ' .

, '~argent suggests this hypothesis as a means of generating a second-order auidregressive model for employment from a cost-of-adjustment model.

wages. Then

which introduces a first-order autoregressive error into the dynamic employment function (16), and generates a second-order auto-regressive representation of employment.

The terms on the right-hand side of equation (16) depend on the definitions and forecasting equations for alternative wages, flight activity, nonlabor input prices, and contract wages. On the basis of the evidence reported in Section I, I assume that the alternative wage for airline mechanics is represented by the average hourly wage rate in manufacturing (apart from trend and seasonal factors). As a measure of flight activity, I use the level of domestic departures. Finally, for lack of suitable data, I assume that nonlabor input prices (9,) are captured by trend and sea-sonal factors. Thls assumption is especially problematic if the main substitute for in- house employment is subcontracted maintenance. and if the rice of subcontracted maintenance is correlated with mechanics' wage rates.

~ u i l d i n ~ the results in Ion Section I, adopt the following second-order autoregressive forecasting system for detrended and deseasonalized departures, manufacturing wages, contract wages, and consumer prices:

(17a) l o g F , = ~ l l o g F , ~ l + $ J 2 1 0 g F , 2 + u l , ,

(17b) log a , = a1log a,-, + a210g a,-,

(17c) l o g ~ , = S , l o g w , ~ ~ + S ~ l o g w , ~ ,

+ 411% a,- , + #,log a,-2

(I7d] log PI= 77i10gPI-1


where the vector of residuals (u,,, u,,, u,,, u,,) is assumed to be serially uncorre-lated. In t h s forecasting system, aggregate prices and manufacturing wages depend on their own lagged values and lagged values of each other, while departures are forecast by a univariate second-order autoregression. Contract wages depend on their own lagged values as well as lagged values of manufacturing wages and consumer prices. The forecasting equation for contract wages can be interpreted as a log-linear approximation to the first-order condition (7) for optimal contract wages, although I do not restrict the coefficients of the equation in any way. The evidence that alternative wages help forecast contract wages is more consistent with the Cobb-Douglas preference specification than the expected utility specification, although neither model provides a ready interpretation of the role of prices in forecasting contract wage rates.29

The system of second-order forecasting equations (17) generate the following expressions:

33

( 1 8 4 (1- AP) C ( h P ) ' ~ , l o g ~ , + ,J = o

2 9 ~ h etheoretical model assumes that contract wage rates are adjusted every period, whereas mechanics wage rates are set in two- or three-year nominal contracts. This suggests that there may be a cost of adjusting contract wage rates that is missing from the model.

where the B,, are known functions of the coefficients in equations (17a)-(17d). Sub-stituting these equations into (16), performing a transformation to eliminate serial correlation in the productivity shock E , , and using (17a)-(17d) to substitute for current values of departures, prices and wages in terms of lagged values and innovations in these variables yields the reduced-form employment equation implied by the model. T h s reduced form contains two lagged values of employment, and each of the exogenous variables (including contract wages), as well as a residual that is a combination of the unanticipated productivity shock (, and the current forecast errors u,,, u,,, u,,, and u4,. The coefficients of the reduced-form equation depend on the coefficients of equations (16) and (18), the adjustment parameter A , and the serial correlation coefficient p of the unobserved productivity shock.,' The dynamic properties of employment, however, depend solely on X and p. The first- order autoregressive coefficient of employ-ment is the sum of X and p, while the second-order autoregressive coefficient is the negative of their product.

To illustrate the implications of the model for the reduced-form employment equation, it is useful to consider two polar models of employment determination: the labor de-mand model in whch the relevant opportunity cost of contract labor is the contract wage; and the strong form efficient contract model in which the relevant opportunity cost is the alternative wage rate. In the labor demand model, b, = 0 in equation (16) and the alternative wage effects employment only through the forecasting equation for contract wages. If future contract wages depend positively on manufacturing wages, for example, then employment should depend negatively on manufacturing wages, at least in the long run. The evidence in Tables 2 and 4, however, shows that manufacturing wages have a positive long-run impact on contract wages, and a positive long-run effect on employ-

''A detailed derivation of the reduced-form employment equation is presented in Appendix I.

VOL. 76 NO. 5 CARD: EFFICIENT CONTRACTS WITH COSTLY ADJUSTIWEhrT 1063

ment. In the strong form efficient contract, on the other hand, N,* is independent of contract wages and depends only on the level of alternative wages. This model is also rejected by the unrestricted employment regressions in Table 4, whch show a negative impact of contract wages on employment, holding constant manufacturing wages. More formal tests between these two polar models, and tests of the overidentifying restrictions implied by the general contracting model, are presented in the next section.

111. Empirical Analysis of the Dynamic Contracting Model

The model of employment determination developed in Section I1 consists of the prediction equations for contract wages, alternative wages and departures (equations (17a)-(17d)), together with the reduced-form employment equation implied by (16). This section presents estimation results based on fitting t h s five-equation system to aggregate quarterly data on manufacturing wages and consumer prices as well as firm-specific data on contract wages, employment, and departures for the seven airline firms. For simplicity, the firm-specific data are deseasonalized and detrended prior to estimation. This permits unrestricted airline-specific constants, trends, and seasonals to be fitted outside of the main estimation step, at the cost of some potential bias in the estimated standard errors.

In addition, rather than estimate equations for the airline-specific data and the aggregate data simultaneously, I have estimated the manufacturing wage and con-sumer price equations separately over a longer sample period (1964:III-1978:IV), and then used the estimated parameters as known constants in the calculation of the restricted employment equation. The model is therefore treated as a three-equation system for employment, wages, and departures, with known forecasting equations for ag-gregate wages and prices.

The employment, wage, and departures equations for each of the seven airline firms (21 equations in all) are fitted to detrended

and deseasonalized data by a two-step non- linear generalized least squares p r ~ c e d u r e . ~ ~ The second-stage estimates minimize the weighted residuals of the twenty-one-equation system, using as weights the inverse covariance matrix formed by the unre-stricted least-squares residuals. Following A. Ronald Gallant and Dale Jorgenson (1979), a goodness-of-fit test is constructed by comparing the weighted sum of squares of the restricted model to the weighted sum of squares of the unrestricted model.

Unrestricted vector-autoregressive repre-sentations of airline-specific departures, wages, and employment are presented in the first two columns of Table 7.32 Column 1 contains estimates of the three-equation system when lagged prices are excluded from the wage and employment equations, whle column 2 contains estimates of the system when lagged prices are included in these two equations. The coefficient estimates are very similar to the corresponding estimates in Tables 2, 4, and 6 obtained by fitting the system equation-by-equation to unadjusted data.

Columns 3 and 4 contain the restricted reduced-form parameter estimates associated with the labor demand version of equation (16). The corresponding structural parameter estimates are presented in columns 1 and 2 of Table 8. In t h s version of the contracting model, the relevant opportunity cost of labor is the contract wage rate, and manufacturing wages enter the employment equation for airline mechanics only insofar as they help

3 1 ~ san alternative to this estimation procedure, the model can also be estimated by applying instrumental variables techniques to the first-order condition for contract employment. The instrumental variables procedure has the advantage that closed-form solutions for the optimal employment choice are not required. The ex- plicit solution procedure adopted here, on the other hand, has the advantage of offering a direct interpretation of the reduced-form system for departures, wages, and employment.

32These unrestricted representations incorporate a variety of exclusion restrictions (for example, lagged employment is not included in the departures equation). Conditional on these exclusion restrictions, however, the estimates are unrestricted.


TABLE7-REDUCED-FORM PARAMETER FOR DEPARTURES, EMPLOYMENT:ESTIMATES WAGES, SEVENDOMESTIC 1969:I I I -1976:IVaAIRLINES

Restricted Reduced ~ o r m s ~

Strong Form General Unrestricted Reduced Forms Labor Demand Model Efficient Contract Model Model

( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 )

Departures Equation: Departures

( t - 1 ) Departures

( t - 2 ) Wage Equation: Contract Wages

( t -1) Contract Wages

( t - 2 ) Manufacturing Wages

( t - 1 ) Manufacturing Wages

( t - 2 ) Consumer Prices

( t 1 )-

Consumer Pnces ( t - 2 )

Employment Equation: Employment

( t - 1 ) Employment

( t - 2 ) Departures

( t 1 )-


Contract Wages ( t - 1 )

Contract Wages ( t - 2 )



Consumer Prices ( t - 1 )

Consumer Prices ( t - 2 )

Log Likelihood -

"Estimated on detrended and deseasonalized data. Observations from strike and immediate poststrike periods are deleted. Estimates are from the second stage of a two-step generalized least squares procedure. The standard errors are shown in parentheses.

b~es t r ic ted reduced forms are conditional on parameter estimates for consumer price and manufacturing wage equations. The estimates in cols. 3 and 4 correspond to the structural estimates in cols. 1 and 2 of Table 8. The estimates in cols. 5 and 6 correspond to the stmctural estimates in cols. 3 and 4 of Table 8. The estimates in col. 7 correspond to the structural estimates in col. 5 of Table 8.

1065 VOL. 76 NO. 5 CARD: EFFICIEKT CONTRACTS WITH COSTL I' ADJUSTMEST

Strong Form General Labor Demand Model Efficient Contract Model Model

Prices Prices Prices Prices Prices Excluded Included Excluded Included Included

(1) (2) (3) (4) ( 5 )

Partial-Adjustment Parameter ( A )

Serial Correlation Parameter ( p )

Output Elasticity ( b , )

Contract Wage Elasticity (h,)

Alternative Wage Elasticity (h , )

Log Likelihood Goodness-of-Fit

against Unrestricted Modelb

aSee notes to Table 7. The standard errors are shown in parentheses. Estimates in cols. 1 and 3 are based on a forecasting equation for contract wages that excludes consumer prices. Estimates in eols. 2. 4, and 5 are based on a forecasting equation for contract wages that includes manufacturing wages and consumer prices. Estimates are conditional on parameter estimates for consumer price and manufacturing wage equations.

b ~ r ~ b a b i l i t yvalue is shown in brackets. The models in cols. 1 and 3 have 4 degrees of freedom. The models in cols. 2 and 4 have 6 degrees of freedom. The model in col. 5 has 5 degrees of freedom.

to predict future contract wages. The model The estimated wage elasticities (parameter is therefore an application of Thomas Sar- b,) for the labor demand model are small gent's dynamic employment demand model and positive, and insignificantly different to firm-specific data, with output taken as from zero. A comparison of the restricted exogenous. The two alternative specifications reduced forms in columns 3 and 4 with the of the labor demand model differ by whether unrestricted reduced forms in columns 1and or not lagged prices are used to forecast 2 suggests several difficulties with the re-future contract wages and future alternative stricted fit. First, the labor demand model wages.33 cannot explain the opposite signs of contract

and manufacturing wages in the reduced- form employment equation, given that future contract wages are positively correlated 33To estimate the reduced-form employment equa-

tion, I set the quarterly discount rate /? to .99. When with manufacturing wages. Second, in the prices are included in the forecasting equations for specification of the model that includes prices wages. I use the following forecasting equations for in the forecasting equation for contract aggregate manufacturing wages (a , ) and consumer wages, the relatively small effects of prices prices ( p,): on employment are difficult to reconcile with

loga, = .701oga,-, + .021oga,-,

- . 52 logp , , + .47logp,.,

logp, =1.79logp,-, - .7810gp,-~ equation, I use the following forecasting equation for

- . I1 log a , ,+ .0210g a ,+ , . manufacturing wages:

When prices are excluded from the wage forecasting loga, =1.0910ga,-~ - .2610ga,_~.


the relatively large effects of prices on expected future contract wages. The goodness-of-fit statistics in the last row of Table 8 suggest that the labor demand interpretation of the employment-wage-output system is strongly rejected by the data.

In contrast to the poor performance of the model in summarizing the effects of wages on employment, the linkage between departures and employment is more successfully explained. The estimated (long-run) output elasticity of employment is between .60 and .80 and is not significantly different from unity. The AR(2) structure of employment is also apparently well-captured by the combination of adjustment costs and first-order serial correlation in demand: a comparison of the restricted and unrestricted reduced-form autoregressive parameters reveals only small differences between them.

Parameter estimates for the strong form efficient contract model, whlch takes the alternative wage rate as the opportunity cost of labor and excludes contract wages from the employment equation altogether, are presented in columns 3 and 4 of Table 8. The associated reduced forms are contained in columns 5 and 6 of Table 7. Again, a comparison of the unrestricted and restricted reduced forms shows that the model has trouble explaining the effects of manufacturing wages on employment. When prices are not used to forecast future manufacturing wage rates, the implied estimate of the elasticity of demand is .29. When prices are included in the wage forecasting equation, on the other hand, the estimated elasticity of demand is - .05. As is the case for the labor demand model of employment determina-tion, the dynamic link between wages and employment is not well explained by the strong form efficient contract model, al-though the departures-employment relation- ship is reasonably well explained by either model.

Finally, estimates of a general contracting model that permits the shadow value of labor to depend on a weighted average of contract and alternative wages are presented in the last columns of Table 7 and Table 8. In t h s general model, prices are included in the forecasting equations for contract wages and

manufacturing wages. A version of the model that excluded prices from the wage equations proved to be ~nident i f ied .~~ Although the general contracting model fits better than either polar model, the estimated wage elasticities of employment are poorly determined and not significantly different from zero. Again. the implied reduced-form coefficients of contract and manufacturing wages in the employment equation are different from the unrestricted coefficients, and the goodness- of-fit test against the unrestricted model is highly significant.

The point estimates imply that mechanics' employment responds negatively to increases in their alternative wage rate, as measured by the manufacturing wage rate, and positively to increases in their contractual wage rate. The latter effect, which may be taken as weak evidence for a positive correlation between contract wages and employment, is consistent with either the expected utility preference specification (2) and some degree of risk aversion, or the Cobb-Douglas specification (3) with 0 <1. From equation (13), the elasticity of employment with respect to the contract wage is b, = a? and the elasticity of contract employment with re-spect to the alternative wage is b, = (1- a)?, where = - y,/(y, + y,) is the constant-output employment elasticity associated with the Cobb-Douglas maintenance technology, and a is the relative weight of contract wages in the expression for the shadow value of labor. The point estimates in column 5 of Table 8 imply a = - .59 and 7 =.-64, although the estimates are extremely imprecise and insignificantly different from zero. For the expected utility specification of workers' preferences, the coefficient - a represents the product of the relative risk-aversion coefficient (6) and the average markup of contract wages over alternative wages (a).If the latter is about .25, the implied estimate of the relative risk-aversion coefficient is

34When prices were excluded from the forecasting equation for contract wages, the sum-of-square function contained a very flat ridge in the b, - b, plane. The fit of the model was essentially unchanged with b, large and negative and b3 large and positive, so long as their ratio was approximately - 60.

1067 VOL. 76 NO. 5 CARD. EFFICIENT CONTRACTS WITH COSTLY ADJUSTMENT

about 2.4. For the Cobb-Douglas preference specification, the coefficient a is an estimate of ( 1- (1 /8 ) ) . The implied value of 8 is .63. These estimates are not unreasonable, although their imprecision is disturbing, as is the failure of the reduced form of the model to reproduce the unrestricted reduced form of the data.

Overall, none of the models considered in t h s paper gives a particularly good fit to the data, particularly with respect to the coefficients of contract or manufacturing wages. In addition, the fact that real contract wage rates and real manufacturing wage rates are both heavily influenced by lagged consumer prices is not easily reconciled with the absence of Aprice effects on e m p l ~ y m e n t . ~ ~ more flexible model of the interactions between contract and alternative wage rates, on one hand, and employment, on the other, is apparently needed to describe the data.

IV. Conclusions

This paper presents an analysis of firm- specific employment and wage outcomes for airline mechanics at seven firms during the period 1969-76. The data possess many of the familiar properties of aggregate wage and employment data, including second-order serial correlation in employment and first-order serial correlation in real wages. Airline mechanics' employment levels are found to be correlated with both their own wage rates, and with average wage rates outside the airline industrj.

A theoretical model is presented that de- scribes the evolution of wages and employment in several alternative settings, including the traditional labor demand setting, where firms take contract wages as exogenous, and an efficient contract setting, where wages and employment are jointly de-termined to minimize employer costs, subject to a utility requirement for workers. The model incorporates costly adjustment of employment over time and emphasizes that

j5Brown and Ashenfelter report similar findings in their investigation of wage and employment outcomes for typographers.

workers' alternative wages can have two effects on employment outcomes: a direct effect on the shadow value of workers' time, and an indirect effect on forecasts of future wage outcomes.

The model gives a straightforward and relatively successful interpretation of the empirical link between airline departures and mechanics' employment. None of the al-ternative versions of the model, however, successfully captures the links between wages and employment. Both the labor demand model and the simplest efficient contracting model, whch equates the marginal product of workers to their alternative wage rate, are rejected in favor of a more general model that includes contract and alternative wages in the employment equation. The parameter estimates for t h s model, however, are extremely imprecise, and the implied reduced- form employment equation fits poorly relative to an unrestricted autoregression. In spite of the promise that simple contracting models might provide a credible interpretation of observed movements in employment and wages, the covariation of employment and wages in these data remains largely unex- plained.

I. Derivation of the Reduced-Form Employment Equation

Let y; = (log F,, log F,- ,,log w,, log w,- ,, log a, , log a,- ,,log p,, log p,- ,) represent the vector of current and once-lagged values of departures, contract wages, manufacturing wages, and prices. Equation (8) can be written as y, = Ay,-, + u,, where u , = (u,,,O, u,,, 0 , u,,,O, u,,, 0), and A is a suitably defined matrix of coefficients. Let e ; = (1,0,.. . ,0). Then

with similar expressions for the fonvard-

1068 THE AMERICAN ECONOMIC REVIEW DECEMBER 1986

moving averages of contract wages and manufacturing wages. Provided that the characteristic roots of A are smaller than (XP)-' in modulus, the infinite sum C,",,(APA)J converges. Assuming thls to be true, let

According to equation (16),

(Al ) l o g N , = A l o g N , ~ , + ( l - A)

where ET is first-order autoregressive with autoregressive parameter p. Let

Performing a transformation of (Al) to eliminate the serial correlation in E: yields

where (, is serially uncorrelated. Finally, substituting for y, into (A2) yields

where 5: = 5, + ( l - A)a*u, is serially un-correlated. In t h s paper I compute the matrix A* numerically and use the resulting estimates to compute the coefficients in (A3) for each value of A , p , b,, b,, b,, and the forecasting coefficients in A.

11. Data Definitions and Sources

1. Wages a) Wage rate information for airline mechanics was

assembled from three sources: contract listings in the Bureau of Labor Statistics' Current Wage Deuelopments (CWD), contract listings and reports in the Bureau of National Affairs' Daily Labor Report (DLR), and copies of the collective bargaining agreements. Typically, contract listings in C WD and DLR include information on percentage and/or absolute wage increases for certified mechanics in each year of the contract. CWD also lists cost-of-living adjustments as they accrue over the life of the contract. Information on wage changes was com- bined with sporadic information on the level of wage rates from both sources to produce a time-series of wage rates by quarter for each airline. For mechanics at Western Airlines, I constructed a time-series of wage rates directly from a complete contract chronology generously provided by the International Brotherhood of Teamsters Airline Division. Wage rates were calcu- lated up to 1984, and compared with the rates listed in recent labor contracts for each airline on file at the National Mediation Board in Washmgton, D.C. In cases where a wage rate was increased retroactively, I use the wage rate that actually prevailed, rather than the retro- active wage rate. In cases where a wage rate increased within a quarter (say in February), I use the unweighted average of the beginning and ending rates as an average quarterly rate.

( i ) American wages are benchmarked to a Septem- ber 1982 rate of 13.53 reported in DLR (March 7, 1983). New contracts were negotiated March 1969 (CWD, April 1969), May 1971 (CWD, July 1971), May 1974 (CWD, May 1974), and June 1975 (CWD, August 1975).

( i r ) Braniff wages are benchmarked to a rate of 4.14 (excluding COLA) in January 1969 reported in DLR (May 6, 1969). New contracts were negotiated May 1969 ( D L R , May 6,1969), September 1972 ( C WD, November 1972), November 1973 (CWD, January 1974) and March 1976 (CWD, May 1976).

(iii) Continental wages are benchmarked to a rate of 4.14 (excluding COLA) in January 1969. New contracts were negotiated September 1969 (CWD, October 1969), August 1972, August 1974 (CWD, September 1974) and January 1976 (CWD, March 1976).

(iu) Eastern wage rates are benchmarked to a rate of 7.69 (excluding COLA) in November 1975 reported in DLR (July 12, 1974). New contracts were negotiated May 1969 (DLR, May 2, 1969). October 1972 (CWD, January 1973, and later Payboard rulings in CWD, May 1973), July 1974 (DLR, July 12, 1974). and January 1976 ( C WD, March 1976).

(0 ) Trans World wage rates are benchmarked to a rate of 7.67 (excluding COLA) in May 1975 reported in DLR (March 13, 1975). New contracts were negotiated January 1970 (CWD, February 1970), December 1972 (CWD, February 1973), February 1975 (DLR, March 13,1975), and September 1976 (CWD, November 1976).

(wr) United wage rates are benchmarked to a rate of 7.50 (excluding COLA) in January 1975, reported in

1069 VOL. 76 NO. 5 CARD: EFFICIENT CONTRACTS WITII COSTLY A DJC'STMENT

DLR (May 3, 1974). New contracts were negotiated October 1969 (CWD, November 1969). August 1972 (CWD, October 1972), May 1974 (CWD, June 1974) and December 1975 (CWD, February 1976).

(oii) Western wage rates are taken directly from collective bargaining agreements dated November 1968 (negotiated August 1969); dated November 1971 (negotiated July 1972); and dated November 1973 (negotiated May 1974). Information on COLA payments under the Western agreements was taken from CWD (various issues).

b) Wage rate information for maintenance mechanics in manufacturing industries is taken from the Bureau of Labor Statistics' Area Wage Surcey. Results of the annual survey, which is administered in different months in different cities, are published in the following BLS Bullerrris: 1968-No. 1575; 1969-No. 1625; 1970- No. 1660; 1971-No. 1685; 1972-No. 1725: 1973-No. 1775: 1974-No. 1850; 1975-No. 1900; 1976-No. 1950 (Washington: USGPO). I used both the average wage rate for all cities, and wage rates for the following city-airline pairs: Dallas/Fort Worth-Braniff (weighted average of Dallas (.67) and Fort Worth (.33) from 1968 to 1973); Miami-Eastern: Oklahoma City (in lieu of Tulsa)-American: St. Louis-Trans World; Los Angeles-Continental and Western; San Francisco-United. The annual wage series were interpolated lin- early using the 1968 values for first quarter 1969 for cities where the survey is administered in late fall (Dal- las/Fort Worth. mami , Oklahoma City, San Francisco) and using the 1969 values for first quarter 1969 for St. Louis and Los Angeles, where the surveys are administered earlier in the year. The average wage rate for all cities, whch the BLS reports as an average for February, was interpolated using the 1969 wage for first quarter 1969.

C) Average straight-time hourly earnings of production workers in manufacturing represent quarterly averages of monthly earnings as reported in U.S. Bureau of Commerce, Busrtiess Statistics (1979 ed.) (Washington: USGPO, 1980, p. 228).

d) Wage rates of licensed mechanics at Hoeing are taken from the BLS Wage Chronology for Boeing (Washington State) and the International Association of Machinists, published in BLS BuNetirl No. 1895 (Washington: USGPO, 1976). Rates for mechanics are listed as basic hourly rates for labor grade 10 in Table 2c, p, 19.

2. Flight Information Flight information is taken from monthly informa-

tion in Civil Aeronautics Board, Air Carrier Traflc Sratisrics (Washington: CAB).

a) Departures: Aircraft revenue departures per-formed in each quarter in scheduled domestic oper-ations.

b) Available Seat Miles: Total available seat miles in each quarter in scheduled domestic operations.

c) Revenue Passenger Miles: Total revenue passenger miles in each quarter in scheduled domestic operations.

d) Donlestic Flight Hours: Total aircraft revenue hours in scheduled domestic operations and nonscheduled domestic operations.

e) Total Flight Hours: Total aircraft revenue hours in all services (domestic and international; scheduled and nonscheduled).

Precise definitions of these variables are contained in each issue of 4 i r Carrier Traffic Statistic:.

3. Employment Information Employment and payroll information is taken from

the "Form-41" reports filed monthly by each airline. Prior to 1977, the March, June, September, and Decem- ber Form 41 reports contained a quarterly P-10 report on employment and payroll by category of worker. The number of mechanics is taken from employment totals for maintenance labor (P-10 Account Number 25). In Figure 1, "pilots" include pilots and copilots (P-10 Account Number 23) and flight engineers (P-10 Account Number 5124); "flight attendants" represent passenger service flying personnel (P-10 Account Number 5524). Form 41 reports are on file at the Department of Transportation in Washington D.C. (Formerly, these reports were housed at the Civil Aeronautics Board.) The 1969 information was taken from microfilm ar-chives of the Form 41 reports.

4. Miscellaneous Information a) Real GNP (seasonally adjusted) is taken from

U.S. Bureau of Commerce Bu~rness Statistrcs (1979 ed.) (Washington: USGPO. 1980, p. 251).

b) The Consumer Price Index (All Items) is taken from OECD, Historical Statistics 1Yh0- 79 (Paris: OECD, 1980. p. 73).

c) A price index for don~estic passenger fares was constructed from information contained in Atinual Re- ports of various airline firms, and from the Civil Aeronautics Board .Annual Report (Washington: CAB). various issues. Between January 1969 and December 1976 the major changes in fares were as follows:

February 20. 1969: 3.8 percent general increase October 1 , 1969: 6.35 percent general increase October 15, 1970: 3.0 percent general increase May 1, 1971: 6.0 percent general increase September 5, 1972: 2.7 percent general increase December 1, 1973: 5.0 percent general increase November 1. 1974: 4.0 percent general increase November 15, 1975: 3.0 percent general increase.

The Civil Aeronautics Board also granted an 8.0 percent general fare increase in a series of three incre- ments during 1976. I assume that these increases took the form of a 2.0 percent increase on April 1, 1976, a 3.0 percent general increase on July 1, 1976, and a 2.0 percent general increase on October 1, 1976.

d) An index of jet fuel prices was constructed from annual average jet fuel prices per gallon reported in Civil Aeronautics Board, "Long Term Fuel Expense. Consumption. Unit Prices and Total Expense, System Trunks and Locals," CAB Financial and Cost Analysis Division (Manuscript dated March 21, 1983). index- linked within each year to quarterly averages of monthly producer prices for refined petroleum products, as reported in OECD, 1Ii.storical Sratrsrits 1960- 79 (Paris: OECD. 1980, p. 73). The CAB reports average annual fuel prices (in cents per gallon) as 12.23 in 1972. 12.85 in 1973, 21.95 in 1974. 27.37 in 1975, 30.42 in 1976, and

1070 T H L A MERICA N ECONOMIC R E V l EW DECEMBER 1986

35.24 in 1977. I used the producer price index for refined petroleum, indexed-linked to the 1972 average price reported by the CAB, to estimate quarterly prices for jet fuel in 1969, 1970, and 1971. Fuel prices reported by the various individual airlines in their Annual Re-ports are very similar to the CAB average prices. For example, in 1977, Western reported an average price of .36. United reported an average price of .35, Trans World reported an average price of ,375 and Continen- tal reported an average price of ,359 per gallon.

e) An index of aircraft parts prices was constructed from the monthly industry wholesale price index for "General Purpose Machnery and Parts" (Commodity Group 114) from Bureau of Labor Statistics Wholesale Prices and Price It~drxes (Washngton: USGPO). various issues.

f ) Fleet composition information by airline was interpolated from annual fleet composition information contained in the Federal Aviation Authority Sratrstical Ha~idbookof A~*iatiorz(Washngton: FAA). various issues.

g) Airline-specific unemployment rates are based on quarterly averages of monthly insured unemployment rates for the following city-airline pairs: Los Angeles-Continental and Western: San Francisco-United: Miami-Eastern; St. Louis-Trans World: Dal- las/Fort Worth-Braniff. I used the insured unemployment rate for Oklahoma in lieu of city-specific information for Tulsa-American. Insured unemployment rates by city and state were taken from BLS Cn~ployn~entand Earrnnys (Washington: USGPO) various issues.

A complete listing of the data is available from the author on request. Copies of the computer programs used to generate the estimates in Tables 7 and 8 are also available on request.

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You have printed the following article:

Efficient Contracts with Costly Adjustment: Short-Run Employment Determination forAirline MechanicsDavid CardThe American Economic Review, Vol. 76, No. 5. (Dec., 1986), pp. 1045-1071.Stable URL:


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1 Implicit Contracts and Underemployment EquilibriaCostas AzariadisThe Journal of Political Economy, Vol. 83, No. 6. (Dec., 1975), pp. 1183-1202.Stable URL:

http://links.jstor.org/sici?sici=0022-3808%28197512%2983%3A6%3C1183%3AICAUE%3E2.0.CO%3B2-B

1 Wages and Employment under Uncertain DemandMartin Neil BailyThe Review of Economic Studies, Vol. 41, No. 1. (Jan., 1974), pp. 37-50.Stable URL:

http://links.jstor.org/sici?sici=0034-6527%28197401%2941%3A1%3C37%3AWAEUUD%3E2.0.CO%3B2-4

1 Efficient Wage Bargains Under Uncertain Supply and DemandRobert E. Hall; David M. LilienThe American Economic Review, Vol. 69, No. 5. (Dec., 1979), pp. 868-879.Stable URL:

http://links.jstor.org/sici?sici=0002-8282%28197912%2969%3A5%3C868%3AEWBUUS%3E2.0.CO%3B2-T

1 Wage Bargaining and EmploymentIan M. McDonald; Robert M. SolowThe American Economic Review, Vol. 71, No. 5. (Dec., 1981), pp. 896-908.Stable URL:

http://links.jstor.org/sici?sici=0002-8282%28198112%2971%3A5%3C896%3AWBAE%3E2.0.CO%3B2-%23

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1 Optimal Labour Contracts under Asymmetric Information: An IntroductionOliver D. HartThe Review of Economic Studies, Vol. 50, No. 1. (Jan., 1983), pp. 3-35.Stable URL:

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1 Implicit Contracts: A SurveySherwin RosenJournal of Economic Literature, Vol. 23, No. 3. (Sep., 1985), pp. 1144-1175.Stable URL:

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1 Bargaining Power, Fear of Disagreement, and Wage Settlements: Theory and Evidence fromU.S. IndustryJan SvejnarEconometrica, Vol. 54, No. 5. (Sep., 1986), pp. 1055-1078.Stable URL:

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1 Testing the Efficiency of Employment ContractsJames N. Brown; Orley AshenfelterThe Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference.(Jun., 1986), pp. S40-S87.Stable URL:

http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

1 Testing between Competing Models of Wage and Employment Determination in UnionizedMarketsThomas E. MaCurdy; John H. PencavelThe Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference.(Jun., 1986), pp. S3-S39.Stable URL:

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10 Time Series Representations of Economic Variables and Alternative Models of the LabourMarketOrley Ashenfelter; David CardThe Review of Economic Studies, Vol. 49, No. 5, Special Issue on Unemployment. (1982), pp.761-781.Stable URL:

http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9

12 Estimation of Dynamic Labor Demand Schedules under Rational ExpectationsThomas J. SargentThe Journal of Political Economy, Vol. 86, No. 6. (Dec., 1978), pp. 1009-1044.Stable URL:

http://links.jstor.org/sici?sici=0022-3808%28197812%2986%3A6%3C1009%3AEODLDS%3E2.0.CO%3B2-E

18 Miners' Wages in Post-War Britain: An Application of a Model of Trade Union BehaviourAlan A. Carruth; Andrew J. OswaldThe Economic Journal, Vol. 95, No. 380. (Dec., 1985), pp. 1003-1020.Stable URL:

http://links.jstor.org/sici?sici=0013-0133%28198512%2995%3A380%3C1003%3AMWIPBA%3E2.0.CO%3B2-V

23 The Estimation of Partial Adjustment Models with Rational ExpectationsJohn KennanEconometrica, Vol. 47, No. 6. (Nov., 1979), pp. 1441-1455.Stable URL:

http://links.jstor.org/sici?sici=0012-9682%28197911%2947%3A6%3C1441%3ATEOPAM%3E2.0.CO%3B2-X

References

Time Series Representations of Economic Variables and Alternative Models of the LabourMarketOrley Ashenfelter; David CardThe Review of Economic Studies, Vol. 49, No. 5, Special Issue on Unemployment. (1982), pp.761-781.Stable URL:

http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9




http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9&origin=JSTOR-pdf

http://links.jstor.org/sici?sici=0022-3808%28197812%2986%3A6%3C1009%3AEODLDS%3E2.0.CO%3B2-E&origin=JSTOR-pdf

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http://links.jstor.org/sici?sici=0034-6527%281982%2949%3A5%3C761%3ATSROEV%3E2.0.CO%3B2-9&origin=JSTOR-pdf

Implicit Contracts and Underemployment EquilibriaCostas AzariadisThe Journal of Political Economy, Vol. 83, No. 6. (Dec., 1975), pp. 1183-1202.Stable URL:

http://links.jstor.org/sici?sici=0022-3808%28197512%2983%3A6%3C1183%3AICAUE%3E2.0.CO%3B2-B

Wages and Employment under Uncertain DemandMartin Neil BailyThe Review of Economic Studies, Vol. 41, No. 1. (Jan., 1974), pp. 37-50.Stable URL:

http://links.jstor.org/sici?sici=0034-6527%28197401%2941%3A1%3C37%3AWAEUUD%3E2.0.CO%3B2-4

Testing the Efficiency of Employment ContractsJames N. Brown; Orley AshenfelterThe Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference.(Jun., 1986), pp. S40-S87.Stable URL:

http://links.jstor.org/sici?sici=0022-3808%28198606%2994%3A3%3CS40%3ATTEOEC%3E2.0.CO%3B2-5

Miners' Wages in Post-War Britain: An Application of a Model of Trade Union BehaviourAlan A. Carruth; Andrew J. OswaldThe Economic Journal, Vol. 95, No. 380. (Dec., 1985), pp. 1003-1020.Stable URL:

http://links.jstor.org/sici?sici=0013-0133%28198512%2995%3A380%3C1003%3AMWIPBA%3E2.0.CO%3B2-V

Efficient Wage Bargains Under Uncertain Supply and DemandRobert E. Hall; David M. LilienThe American Economic Review, Vol. 69, No. 5. (Dec., 1979), pp. 868-879.Stable URL:

http://links.jstor.org/sici?sici=0002-8282%28197912%2969%3A5%3C868%3AEWBUUS%3E2.0.CO%3B2-T

Optimal Labour Contracts under Asymmetric Information: An IntroductionOliver D. HartThe Review of Economic Studies, Vol. 50, No. 1. (Jan., 1983), pp. 3-35.Stable URL:

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The Estimation of Partial Adjustment Models with Rational ExpectationsJohn KennanEconometrica, Vol. 47, No. 6. (Nov., 1979), pp. 1441-1455.Stable URL:

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Wage Bargaining and EmploymentIan M. McDonald; Robert M. SolowThe American Economic Review, Vol. 71, No. 5. (Dec., 1981), pp. 896-908.Stable URL:

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Testing between Competing Models of Wage and Employment Determination in UnionizedMarketsThomas E. MaCurdy; John H. PencavelThe Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor Conference.(Jun., 1986), pp. S3-S39.Stable URL:

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The Tradeoff Between Wages and Employment in Trade Union ObjectivesJohn H. PencavelThe Quarterly Journal of Economics, Vol. 99, No. 2. (May, 1984), pp. 215-231.Stable URL:

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Implicit Contracts: A SurveySherwin RosenJournal of Economic Literature, Vol. 23, No. 3. (Sep., 1985), pp. 1144-1175.Stable URL:

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Estimation of Dynamic Labor Demand Schedules under Rational ExpectationsThomas J. SargentThe Journal of Political Economy, Vol. 86, No. 6. (Dec., 1978), pp. 1009-1044.Stable URL:

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Bargaining Power, Fear of Disagreement, and Wage Settlements: Theory and Evidence fromU.S. IndustryJan SvejnarEconometrica, Vol. 54, No. 5. (Sep., 1986), pp. 1055-1078.Stable URL:

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efficient contracts with costly adjustment: short-run

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